The previous result has been improved in [1]}, where the authors showed that for \(0<q<1,\,p=2q,\)  \(\alpha >0\)  and \(a=1\)  one has:
\(\displaystyle g\left(x(t)\right) - \min g =O\left(\frac{1}{t^{2q}}\right) \mbox{ as }t\rightarrow +\infty ,\) 
\(\displaystyle \Vert \dot{x}(t)\Vert  =O\left(\frac{1}{t^{\frac{q+1}{2}}}\right) \mbox{ as }t\rightarrow +\infty \) 
and
\( \lim _{t \rightarrow \infty }{\Vert  x(t) - x^\ast \Vert } = 0.\) 
More precisely, by denoting \(x_t\)  the unique minimizer of the strongly convex function \(g(x)+\frac{1}{2t^p}\Vert x\Vert ^2\) , it is shown in [1]} that \(\Vert  x(t) - x_t \Vert =O\left(\frac{1}{t^{\frac{1-q}{2}}}\right) \mbox{ as }t\rightarrow +\infty \)  and this implies that
\( \lim _{t \rightarrow \infty }{\Vert  x(t) - x^\ast \Vert } = 0.\) 
